:- use_module(library('clp/bounds')).

sudoku(Grid, Vars) :-

  Vars = 
   [
    A1,A2,A3,A4,A5,A6,A7,A8,A9,
    B1,B2,B3,B4,B5,B6,B7,B8,B9,
    C1,C2,C3,C4,C5,C6,C7,C8,C9,
    D1,D2,D3,D4,D5,D6,D7,D8,D9,
    E1,E2,E3,E4,E5,E6,E7,E8,E9,
    F1,F2,F3,F4,F5,F6,F7,F8,F9,
    G1,G2,G3,G4,G5,G6,G7,G8,G9,
    H1,H2,H3,H4,H5,H6,H7,H8,H9,
    I1,I2,I3,I4,I5,I6,I7,I8,I9
   ],

  Vars in 1..9,

  all_different([A1,A2,A3,A4,A5,A6,A7,A8,A9]),
  all_different([B1,B2,B3,B4,B5,B6,B7,B8,B9]),
  all_different([C1,C2,C3,C4,C5,C6,C7,C8,C9]),
  all_different([D1,D2,D3,D4,D5,D6,D7,D8,D9]),
  all_different([E1,E2,E3,E4,E5,E6,E7,E8,E9]),
  all_different([F1,F2,F3,F4,F5,F6,F7,F8,F9]),
  all_different([G1,G2,G3,G4,G5,G6,G7,G8,G9]),
  all_different([H1,H2,H3,H4,H5,H6,H7,H8,H9]),
  all_different([I1,I2,I3,I4,I5,I6,I7,I8,I9]),

  all_different([A1,B1,C1,D1,E1,F1,G1,H1,I1]),
  all_different([A2,B2,C2,D2,E2,F2,G2,H2,I2]),
  all_different([A3,B3,C3,D3,E3,F3,G3,H3,I3]),
  all_different([A4,B4,C4,D4,E4,F4,G4,H4,I4]),
  all_different([A5,B5,C5,D5,E5,F5,G5,H5,I5]),
  all_different([A6,B6,C6,D6,E6,F6,G6,H6,I6]),
  all_different([A7,B7,C7,D7,E7,F7,G7,H7,I7]),
  all_different([A8,B8,C8,D8,E8,F8,G8,H8,I8]),
  all_different([A9,B9,C9,D9,E9,F9,G9,H9,I9]),

  all_different([A1,A2,A3,B1,B2,B3,C1,C2,C3]),
  all_different([A4,A5,A6,B4,B5,B6,C4,C5,C6]),
  all_different([A7,A8,A9,B7,B8,B9,C7,C8,C9]),
  all_different([D1,D2,D3,E1,E2,E3,F1,F2,F3]),
  all_different([D4,D5,D6,E4,E5,E6,F4,F5,F6]),
  all_different([D7,D8,D9,E7,E8,E9,F7,F8,F9]),
  all_different([G1,G2,G3,H1,H2,H3,I1,I2,I3]),
  all_different([G4,G5,G6,H4,H5,H6,I4,I5,I6]),
  all_different([G7,G8,G9,H7,H8,H9,I7,I8,I9]),

  grid(Grid, Vars),

  label(Vars).


grid([],[]) :- !.
grid([0|Q1],[_|Q2]) :-
  !,
  grid(Q1,Q2).


grid([Val|Q1],[Var|Q2]) :-
  !,
  Var #= Val,
  grid(Q1,Q2).


sudoku_valide(Vars) :-
    sudoku(
        [1, 0, 0, 0, 8, 5, 0, 4, 0,
        7, 9, 0, 0, 1, 0, 3, 0, 0,
        0, 3, 4, 0, 0, 0, 6, 0, 0,
        0, 5, 3, 7, 9, 0, 0, 0, 0,
        4, 0, 7, 0, 5, 0, 1, 0, 3,
        0, 0, 0, 0, 3, 6, 8, 7, 0,
        0, 0, 5, 0, 0, 0, 2, 3, 0,
        0, 0, 1, 0, 2, 0, 0, 6, 7,
        0, 7, 0, 9, 4, 0, 0, 0, 1],
    Vars).

sudoku_send_response(Grid) :-
    sudoku(Grid, Vars),
    write('solution(s)!'), nl.
sudoku_send_response(Grid) :-
    not(sudoku(Grid, Vars)),
    write('no solution'),nl.